相关论文: Chiral Tetrahedrons as Unitary Quaternions: Molecu…
The algebraic structure of central molecular chirality can be achieved starting from the geometrical representation of bonds of tetrahedral molecules, as complex numbers in polar form, and the empirical Fischer projections used in organic…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…
On the basis of empirical Fischer projections, we developed an algebraic approach to central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral…
Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here the description of central chirality for tetrahedral molecules using a geometrical approach based on…
We propose a predictive building-up of tetrahedral molecules, based on a previously derived chirality index, which characterizes a tetrahedral molecule, with n chiral centers, as achiral, diastereoisomer, or enantiomer as a function of the…
The construction of algebraic structure of central molecular chirality is provided starting from the empirical Fischer projections for tetrahedrons. A matrix representation is given and the algebra of O(4) orthogonal group for rotations and…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
In this talk I discuss and clarify some issues concerning chiral and nonchiral properties of the one-dimensional supermultiplets of the N-Extended Supersymmetry. Quaternionic chirality can be defined for N=4,5,6,7,8. Octonionic chirality…
We review the concept of chirality and charge for particles and antiparticles. We point out that the commonly accepted equivalence of particles and antiparticles - with difference only in the opposite signs of their charges, which follows…
We propose an approach to sensitively probe the chirality of molecules by measuring their coherent optical absorption spectra. It is shown that quantum dynamics of the cyclic three-level chiral molecules driven by appropriately-designed…
The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral like properties of nuclear systems. To a…
General features of microscopic and macroscopic chiral structures can be discussed under the standard of orthogonal group theory. Configuration space of systems, not physical space, is taken into account. This change of perspective allows…
We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
Electromagnetic properties of quark-like particles are examined in a classical field model involving extended dual electromagnetic fields. These can have fractional charges and a confining potential that derives essentially completely from…
We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…